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Network Working Group                                    A. Adamantiadis
Internet-Draft                                                    libssh
Intended status: Informational                              S. Josefsson
Expires: September 2, 2016                                        SJD AB
                                                           March 1, 2016


  Secure Shell (SSH) Key Exchange Method using Curve25519 and Curve448
                     draft-josefsson-ssh-curves-04

Abstract

   How to implement the Curve25519 and Curve448 key exchange methods in
   the Secure Shell (SSH) protocol is described.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   time.  It is inappropriate to use Internet-Drafts as reference
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   This Internet-Draft will expire on September 2, 2016.

Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   described in the Simplified BSD License.





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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Key Exchange Methods  . . . . . . . . . . . . . . . . . . . .   3
     2.1.  Shared Secret Encoding  . . . . . . . . . . . . . . . . .   3
   3.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   4
   4.  Security Considerations . . . . . . . . . . . . . . . . . . .   4
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   4
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   5
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .   5
     6.2.  Informative References  . . . . . . . . . . . . . . . . .   5
   Appendix A.  Copying conditions . . . . . . . . . . . . . . . . .   5
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   6

1.  Introduction

   In [Curve25519], a new elliptic curve function for use in
   cryptographic applications was introduced.  In [Ed448-Goldilocks] the
   Ed448-Goldilocks curve (also known as Curve448) is described.  In
   [RFC7748], the Diffie-Hellman functions using Curve25519 and Curve448
   are specified.

   Secure Shell (SSH) [RFC4251] is a secure remote login protocol.  The
   key exchange protocol described in [RFC4253] supports an extensible
   set of methods.  [RFC5656] describes how elliptic curves are
   integrated in SSH, and this document reuses those protocol messages.

   This document describes how to implement key exchange based on
   Curve25519 and Curve448 in SSH.  For Curve25519 with SHA-256
   [RFC4634], the algorithm we describe is equivalent to the privately
   defined algorithm "curve25519-sha256@libssh.org", which is currently
   implemented and widely deployed in libssh and OpenSSH.  The Curve448
   key exchange method is novel but similar in spirit, and we chose to
   couple it with SHA-512 [RFC4634] to further separate it from the
   Curve25519 alternative.

   This document provide Curve25519 as the prefered choice, but suggests
   that the fall back option Curve448 is implemented to provide an hedge
   against unforseen analytical advances against Curve25519 and SHA-256.
   Due to different implementation status of these two curves (high-
   quality free implementations of Curve25519 has been in deployed use
   for several years, while Curve448 implementations are slowly
   appearing), it is accepted that adoption of Curve448 will be slower.

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].




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2.  Key Exchange Methods

   The key exchange procedure is similar to the ECDH method described in
   chapter 4 of [RFC5656], though with a different wire encoding used
   for public values and the final shared secret.  Public ephemeral keys
   are encoded for transmission as standard SSH strings.

   The protocol flow, the SSH_MSG_KEX_ECDH_INIT and
   SSH_MSG_KEX_ECDH_REPLY messages, and the structure of the exchange
   hash are identical to chapter 4 of [RFC5656].

   The method names registered by this document are "curve25519-sha256"
   and "curve448-sha512".

   The methods are based on Curve25519 and Curve448 scalar
   multiplication, as described in [RFC7748].  Private and public keys
   are generated as described therein.  Public keys are defined as
   strings of 32 bytes for Curve25519 and 56 bytes for Curve448.
   Clients and servers MUST fail the key exchange if the length of the
   received public keys are not the expected lengths, or if the derived
   shared secret only consists of zero bits.  No further validation is
   required beyond what is discussed in [RFC7748].  The derived shared
   secret is 32 bytes when Curve25519 is used and 56 bytes when Curve448
   is used.  The encodings of all values are defined in [RFC7748].  The
   hash used is SHA-256 for Curve25519 and SHA-512 for Curve448.

2.1.  Shared Secret Encoding

   The following step differs from [RFC5656], which uses a different
   conversion.  This is not intended to modify that text generally, but
   only to be applicable to the scope of the mechanism described in this
   document.

   The shared secret, K, is defined in [RFC4253] as a multiple precision
   integer (mpint).  Curve25519/448 outputs a binary string X, which is
   the 32 or 56 byte point obtained by scalar multiplication of the
   other side's public key and the local private key scalar.  The 32 or
   56 bytes of X are converted into K by interpreting the bytes as an
   unsigned fixed-length integer encoded in network byte order.  This
   conversion follows the normal "mpint" process as described in section
   5 of [RFC4251].

   To clarify a corner-case in this conversion, when X is encoded as an
   mpint K, in order to calculate the exchange hash, it may vary as
   follows:






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   o  If the high bit of X is set, the mpint format requires a zero byte
      to be prepended.  In this case, the length of the encoded K will
      be larger.

   o  If X has leading zero bytes, the mpint format requires such bytes
      to be skipped.  In this case, the length of the encoded K will be
      smaller.

3.  Acknowledgements

   The "curve25519-sha256" key exchange method is identical to the
   "curve25519-sha256@libssh.org" key exchange method created by Aris
   Adamantiadis and implemented in libssh and OpenSSH.

   Thanks to the following people for review and comments: Denis Bider,
   Damien Miller, Niels Moeller, Matt Johnston, Mark D.  Baushke.

4.  Security Considerations

   The security considerations of [RFC4251], [RFC5656], and [RFC7748]
   are inherited.

   Curve25519 provide strong security and is efficient on a wide range
   of architectures, and has properties that allows better
   implementation properties compared to traditional elliptic curves.
   Curve448 with SHA-512 is similar, but have not received the same
   cryptographic review as Curve25519, and is slower, but it is provided
   as an hedge to combat unforseen analytical advances against
   Curve25519 and SHA-256.

   The way the derived binary secret string is encoded into a mpint
   before it is hashed (i.e., adding or removing zero-bytes for
   encoding) raises the potential for a side-channel attack which could
   determine the length of what is hashed.  This would leak the most
   significant bit of the derived secret, and/or allow detection of when
   the most significant bytes are zero.  For backwards compatibility
   reasons it was decided not to adress this potential problem.

5.  IANA Considerations

   IANA is requested to add "curve25519-sha256" and "curve448-sha512" to
   the "Key Exchange Method Names" registry for SSH that was created in
   RFC 4250 section 4.10 [RFC4250].








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6.  References

6.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC4250]  Lehtinen, S. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Protocol Assigned Numbers", RFC 4250, DOI 10.17487/
              RFC4250, January 2006,
              <http://www.rfc-editor.org/info/rfc4250>.

   [RFC4251]  Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
              Protocol Architecture", RFC 4251, January 2006.

   [RFC4253]  Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
              January 2006, <http://www.rfc-editor.org/info/rfc4253>.

   [RFC4634]  Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and HMAC-SHA)", RFC 4634, July 2006.

   [RFC5656]  Stebila, D. and J. Green, "Elliptic Curve Algorithm
              Integration in the Secure Shell Transport Layer", RFC
              5656, DOI 10.17487/RFC5656, December 2009,
              <http://www.rfc-editor.org/info/rfc5656>.

   [RFC7748]  Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
              for Security", RFC 7748, DOI 10.17487/RFC7748, January
              2016, <http://www.rfc-editor.org/info/rfc7748>.

6.2.  Informative References

   [Curve25519]
              Bernstein, J., "Curve25519: New Diffie-Hellman Speed
              Records", LNCS 3958, pp. 207-228, February 2006,
              <http://dx.doi.org/10.1007/11745853_14>.

   [Ed448-Goldilocks]
              Hamburg, , "Ed448-Goldilocks, a new elliptic curve", June
              2015, <https://eprint.iacr.org/2015/625>.

Appendix A.  Copying conditions

   Regarding this entire document or any portion of it, the authors make
   no guarantees and are not responsible for any damage resulting from
   its use.  The authors grant irrevocable permission to anyone to use,
   modify, and distribute it in any way that does not diminish the



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   rights of anyone else to use, modify, and distribute it, provided
   that redistributed derivative works do not contain misleading author
   or version information.  Derivative works need not be licensed under
   similar terms.

Authors' Addresses

   Aris Adamantiadis
   libssh

   Email: aris@badcode.be


   Simon Josefsson
   SJD AB

   Email: simon@josefsson.org


































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